The landscape is divided into "countries" (my word) which they call "friendly neighborhoods". In each country, the dimensionless constants such as the gauge couplings and the Yukawa couplings are effectively fixed, but the dimensionful parameters - namely the cosmological constant and the Higgs mass - take many different values and are subject to the anthropic selection.
You know, the cosmological constant has been a big problem in particle physics and people are more ready to accept Weinberg's anthropic argument for this parameter. On the other hand, the hierarchy problem has been solved without the anthropic lack of principles, but it's still OK to view it as a problem. These two numbers - the C.C. and the gap between the Planck scale and the electroweak scale - can both be described as dimensionful parameters.
More quantitatively, they consider a large number "N" of fields, and the number of vacua grows exponentially with "N". On the other hand, the relative fluctuation of the dimensionless couplings go to zero, namely as "1/sqrt(N)" or even faster. They consider various "countries" that describe the Standard Model, the MSSM, and Split SUSY.
The anthropic part of their argument is constructed to have the following results:
- the existence of atoms constrains the ratio of the QCD and the electroweak scale
- because this ratio turns out to be quite small, as in the real world, it solves the hierarchy problem - once again, here it is solved by an anthropic argument
- the mu and the doublet-triplet splitting problems are also claimed to be solved in this setup
- another anthropic argument solves the hierarchy problem by requiring the existence of baryons and vacuum stability
Do I understand it?
Not quite. I'm probably too slow, but the difference between the input and the output is not quite clear to me so far. In field theory, one could have always fine-tuned the parameters - especially those that are potentially problematic, namely the C.C. and the Higgs mass. These constants may be tuned in field theory - the rules allow it. The field theorists have always done it, before they tried to look for explanations of the small values of these parameters.
We may add a completely new decoupled sector - the landscape sector - that gives you some "microscopic feeling" why the different values of these dimensionful parameters are scanned. But from a scientific viewpoint, we're not getting any new prediction beyond what we've inserted, and Occam's razor tells us that we should not add structures if they're not necessary.
We may separate these "nicely, reasonably behaving" parameters from the "bad, hierarchical, strange, dimensionful" parameters, but in field theory we can do it by hand anyway. Surely their mechanism is not meant as a solution to something in field theory where tuning is allowed. It is meant as a toy model for what can arise from a deeper theory - namely string theory.
But the relation of their picture with string theory seems even more confusing to me. They realize very well that the known ensembles of stringy vacua do not fit their definition of the "friendly neighborhood" - i.e. classes of vacua where the "nice dimensionless" parameters are kind of fixed, while the "bad dimensionful" parameters are scanned. They're right that it's probably possible to find classes of vacua which are "friendly". These classes have the advantage that the "nice" parameters can be predicted in them, while the "bad" parameters that normally come out incorrectly are not predicted. ;-)
But I think that the obvious question is then "Why should we be living in a friendly neighborhood?" Is it because Nature is nice and She wants us to be able to calculate? Did She deliberately create us into a special friendly class of vacua - where the things we seem to understand in 2005 are fixed, while the things that we don't understand in 2005 vary - so that we can eventually describe something about Her beauty? This would be really like the proverb about looking for the keys under the lamp only, I think. Well, sure, if we can't do better, it could still make sense to look under the lamp, at least, with some chance to succeed.
Unless there is some other independent mechanism or reason to pick these priviliged vacua - beyond the argument that they're nicer and allow us to calculate a little bit more - I think it is not rationally justified to favor them. Also, I don't quite understand how the specific models they propose differ from the usual minimal models of various types that are still compatible with the observations. Surely that if anyone ever constructed realistic models, she was always checking whether they're compatible with the parameters we see in the Universe, including the mechanisms that had to work in the early and later cosmology. If these things are checked, then - of course - one also satisfies the galactic, atomic, and even the anthropic principle: if all the constants have the right values, we're here.
They use the anthropic argument to replace the "minimality argument" - but I don't quite understand how can the anthropic reasoning ever tell you that the things should be simple. Moreover, the things in the real world are not as simple as possible. Life could probably exist without the third generation of fermions, for example. There may be essentially nothing beyond the Standard Model, and there can be a lot of new physics. In the past, the predictions that there was no new physics were often incorrect - for example if they believed that neutrons, protons, electrons, neutrinos were the only elementary particles.
Both options - no new physics as well as a lot of new physics - lead to viable theories that not only admit life, but that can even agree with the real Universe. I don't understand what the question "how much new physics is there" has to do with the anthropic reasoning, and what is the new justification that tries to twist the answer in some specific direction.
I suppose that the main point is that we should be using a different "measure" to decide which new models are natural and which models are not - but I still don't understand what's exactly the difference of this anthropic approach from the "classical" approach that the models should be constrained by the data that we know and understand well, and they should have freedom about the parameters that we don't understand well, while we're trying to look for the "simplest" models.
Also, I thought that the argument would imply a very strict separation between the dimensionful parameters and the dimensionless ones - the former being a subject to the anthropic principle, while the latter not - and this separation would be respected. But at the end, they also admit that the first family of fermions is rather light, and even though these are described by dimensionless parameters that should be predicted, they also propose an environmental/anthropic explanation for the first family (whose Yukawa couplings are small).
Isn't it then fair to say that we simply demand the anthropic principles and mechanisms - or God - for all things that we don't understand yet and that are unnaturally small, while we expect that the other things will be subject to the old-fashioned rules of predictable physics? Is not such an approach just a less transparent way to admit our ignorance?
One could generalize this type of thinking by allowing a continuous label "S" (strangeness) for each parameter. The higher "S" is, the more the parameter would vary in the neighborhood, and the more it would be a subject to the anthropic selection "rules". Obviously, the things that we find unnatural - especially unnaturally small - would have a high value of "S". Is not such a label equivalent to covering the "success stories" by gold and the "stories of failure" by fog? :-)
I want to wrap this up with a happy end. These guys are so smart that I actually believe that one of their models has a significant chance to be confirmed experimentally. However, I believe that the children in the 22nd century will learn the funny story how Nima, Savas, and Shamit obtained their model by thinking about some weird anthropic ideas, much like Maxwell constructed his equation while he was thinking about the luminiferous aether. ;-) Yes, this statement of mine also implies that with my current understanding, I could not believe the anthropic reasoning even if one of these models turned out to be right.